Electron. J. Differential Equations, Vol. 2017 (2017), No. 170, pp. 1-12.

Solvability of a nonlocal problem for a hyperbolic equation with integral conditions

Anar T. Assanova

We study a nonlocal problem with integral conditions for a hyperbolic equation two independent variables. By introducing additional functional parameters, we investigated the solvability and construction of approximate solutions. The original problem is reduced to an equivalent problem consisting of the Goursat problems for a hyperbolic equation with parameters and the boundary value problem with integral condition for the ordinary differential equations with respect to the parameters. Based on the algorithms for finding solutions to the equivalent problem, we propose algorithms for finding the approximate solutions, and prove their convergence. Coefficient criteria for the unique solvability of nonlocal problem with integral conditions for hyperbolic equation with mixed derivative are also established.

Submitted March 17, 2017. Published July 6, 2017.
Math Subject Classifications: 35L51, 35L53, 35R30, 34B10.
Key Words: Hyperbolic equation; nonlocal problem; integral condition; algorithm; approximate solution.

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Anar T. Assanova
Department of Differential Equations
Institute of Mathematics and Mathematical Modeling
125, Pushkin str., 050010 Almaty, Kazakhstan
email: assanova@math.kz, anarasanova@list.ru

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